{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/21911"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/21911","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Verification of Dade's conjecture for Janko group J(,3)","abstract":"Dade has made a conjecture expressing the number $k(B, d)$ of characters of a given defect d in a given p-block B of a finite group G in terms of the corresponding numbers $k(b, d)$ for blocks b of certain p-local subgroups of G.","abstract_html":"Dade has made a conjecture expressing the number $k(B, d)$ of characters of a given defect d in a given p-block B of a finite group G in terms of the corresponding numbers $k(b, d)$ for blocks b of certain p-local subgroups of G.","abstract_has_math":true,"creators":["Kotlica, Sonja"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:22:58Z","date_published":"2011-05-07T13:22:58Z","updated_at":"2026-07-22T22:25:18Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1996 Kotlica, Sonja"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591198683","AAI9712336","(UMI)AAI9712336"],"render_values":[{"text":"9780591198683","href":null,"code":true},{"text":"AAI9712336","href":null,"code":true},{"text":"(UMI)AAI9712336","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/21911","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kotlica, Sonja"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:22:58Z","10000-01-01","1996"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1996 Kotlica, Sonja"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["9780591198683","AAI9712336","(UMI)AAI9712336","http://hdl.handle.net/2142/21911"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dade has made a conjecture expressing the number $k(B, d)$ of characters of a given defect d in a given p-block B of a finite group G in terms of the corresponding numbers $k(b, d)$ for blocks b of certain p-local subgroups of G.","\"Dade claims that the most complicated form of this conjecture, called the \"\"Inductive Conjecture\"\", will hold for all finite groups if it holds for all covering groups of finite simple groups. In this thesis I verify the inductive conjecture for all covering groups of the third Janko group $J\\sb3$ (in the notation of the Atlas of Finite Groups). This is one step in the inductive proof of the conjecture for all finite groups.\"","The Schur Multiplier of $J\\sb3$ is cyclic of order 3. Hence there are just two covering groups of $J\\sb3,$ namely $J\\sb3$ itself and a central extension $3.J\\sb3$ of $J\\sb3$ by a cyclic group Z of order 3. I treat these two covering groups separately.","\"The outer automorphism group Out($J\\sb3)$ of $J\\sb3$ is cyclic of order 2. In this case Dade affirms in that the Inductive Conjecture for $J\\sb3$ is equivalent to the much weaker \"\"Invariant Conjecture.\"\" Furthermore, Dade has proved that this Invariant Conjecture holds for all blocks with cyclic defect groups. The Sylow p-subgroups of $J\\sb3$ are cyclic of order p for all primes dividing $\\vert J\\sb3\\vert$ except 2 and 3. So I verify the Invariant Conjecture for the two primes $p=2$ and $p=3.$\"","\"The group Out(3.$J\\sb3{\\mid}Z)$ of outer automorphisms of 3.$J\\sb3$ centralizing Z is trivial. In this case Dade affirms that the Inductive Conjecture is equivalent to the \"\"Projective Conjecture.\"\" Again, Dade has shown that this Projective Conjecture holds for all blocks with cyclic defect groups. So I verify the Projective Conjecture for $p=2$ and $p=3.$\"","Made available in DSpace on 2011-05-07T13:22:58Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712336.pdf: 2273357 bytes, checksum: ae4bda95a91deafd754efcd1bedc7a60 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:54:02Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:25:03-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Verification of Dade's conjecture for Janko group J(,3)"]}]}],"canonical_facts":{"dc:creator":["Kotlica, Sonja"],"dc:date":["2011-05-07T13:22:58Z","10000-01-01","1996"],"dc:description":["Dade has made a conjecture expressing the number $k(B, d)$ of characters of a given defect d in a given p-block B of a finite group G in terms of the corresponding numbers $k(b, d)$ for blocks b of certain p-local subgroups of G.","\"Dade claims that the most complicated form of this conjecture, called the \"\"Inductive Conjecture\"\", will hold for all finite groups if it holds for all covering groups of finite simple groups. In this thesis I verify the inductive conjecture for all covering groups of the third Janko group $J\\sb3$ (in the notation of the Atlas of Finite Groups). This is one step in the inductive proof of the conjecture for all finite groups.\"","The Schur Multiplier of $J\\sb3$ is cyclic of order 3. Hence there are just two covering groups of $J\\sb3,$ namely $J\\sb3$ itself and a central extension $3.J\\sb3$ of $J\\sb3$ by a cyclic group Z of order 3. I treat these two covering groups separately.","\"The outer automorphism group Out($J\\sb3)$ of $J\\sb3$ is cyclic of order 2. In this case Dade affirms in that the Inductive Conjecture for $J\\sb3$ is equivalent to the much weaker \"\"Invariant Conjecture.\"\" Furthermore, Dade has proved that this Invariant Conjecture holds for all blocks with cyclic defect groups. The Sylow p-subgroups of $J\\sb3$ are cyclic of order p for all primes dividing $\\vert J\\sb3\\vert$ except 2 and 3. So I verify the Invariant Conjecture for the two primes $p=2$ and $p=3.$\"","\"The group Out(3.$J\\sb3{\\mid}Z)$ of outer automorphisms of 3.$J\\sb3$ centralizing Z is trivial. In this case Dade affirms that the Inductive Conjecture is equivalent to the \"\"Projective Conjecture.\"\" Again, Dade has shown that this Projective Conjecture holds for all blocks with cyclic defect groups. So I verify the Projective Conjecture for $p=2$ and $p=3.$\"","Made available in DSpace on 2011-05-07T13:22:58Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712336.pdf: 2273357 bytes, checksum: ae4bda95a91deafd754efcd1bedc7a60 (MD5) Previous issue date: 1996","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:54:02Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:25:03-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["9780591198683","AAI9712336","(UMI)AAI9712336","http://hdl.handle.net/2142/21911"],"dc:language":["eng"],"dc:rights":["Copyright 1996 Kotlica, Sonja"],"dc:subject":["Mathematics"],"dc:title":["Verification of Dade's conjecture for Janko group J(,3)"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:18Z"}